This applet illustrates the concept of Riemann sum, and shows how it converges to the Riemann integral when the number of partitions grows.
The Riemann sum, or numerical integral is shown in green, and the exact integral is shown in red.
Please notice that GeoGebra is not very powerful at integrating, so, for some functions, the exact integral will crash.
Showing posts with label Calculus. Show all posts
Showing posts with label Calculus. Show all posts
Monday, December 24, 2012
Friday, November 23, 2012
Vector field
This applet allows easy visualization of a two dimensional vector field. The equations for both components can be edited. The length of the plotted vectors can also be changed in order to visualize them more neatly.
Sunday, October 28, 2012
Complex multiplication
This applets illustrates graphically the concept of complex multiplication. As one can easily see, the multiplication of two complex numbers can be performed graphically by multiplying both modules and adding the phase angles.
Sunday, August 19, 2012
Plane curves
This applet allows the user to construct a plane curve using its parametric equations, and display some of its features.
Thursday, May 24, 2012
First order linear differential equation
This applet plots the slopefield of any linear differential equation, and tries to integrate and plot the solution (given the initial condition).
GeoGebra is not very good at integrating, so it will fail in displaying the exact solution very frequently. The slopefield can always be displayed, even for complicated equations.
GeoGebra is not very good at integrating, so it will fail in displaying the exact solution very frequently. The slopefield can always be displayed, even for complicated equations.
Wednesday, May 9, 2012
Number e
This applet demonstrates how the number e can be found by imposing equality between an exponential function and its derivative.
For wich value of a are the two functions identical?
For wich value of a are the two functions identical?
Tuesday, April 3, 2012
Integration
This applet illustrates the concept of definite integral of a function, as the area (with sign) under f(x) and between the vertical limits x = xi and x = xf.
Related applets:
Differentiation.
Related applets:
Differentiation.
Monday, March 26, 2012
Differentiation
This applet illustrates the concept of first derivative, as the best of a series of succesive approximations to the slope in a point.
Sunday, March 18, 2012
Polar coordinates
This applet plots a function specified in polar coordinates, being x the angle in radians.
Monday, March 12, 2012
Taylor series
This applet shows the first 5 Taylor polynomials of a given function. The function is editable, and also the center of the neighborhood.
Observe how the successive orders converge to the given functions.
What happens if the function is a polynomial of order 5 or less?
What happens if the function has discontinuities, like tan(x)?
What happens if the function is not differentiable, like abs(x)?
Observe how the successive orders converge to the given functions.
What happens if the function is a polynomial of order 5 or less?
What happens if the function has discontinuities, like tan(x)?
What happens if the function is not differentiable, like abs(x)?
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